Measurement of Exclusive $\pi^{+}\pi^{-}$ and $\rho^0$ Meson Photoproduction at HERA

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Measurement of Exclusive π ⁺ π ⁻ and ρ ⁰ Meson Photoproduction at HERA

V. Andreev, A. Baghdasaryan, A. Baty, K. Begzsuren, A. Belousov, A. Bolz, V. Boudry, G. Brandt, D. Britzger, A. Buniatyan, et al.

To cite this version:

V. Andreev, A. Baghdasaryan, A. Baty, K. Begzsuren, A. Belousov, et al.. Measurement of Ex- clusive π

π

and ρ

Meson Photoproduction at HERA. Eur.Phys.J.C, 2020, 80 (12), pp.1189.

�10.1140/epjc/s10052-020-08587-3�. �hal-02886864�

DESY 20-080 ISSN 0418-9833 May 2020

Measurement of Exclusive π ⁺ π ⁻ and ρ ⁰ Meson Photoproduction at HERA

H1 Collaboration

Abstract

Exclusive photoproduction of ρ

(770) mesons is studied using the H1 detector at the ep collider HERA. A sample of about 900000 events is used to measure single- and double-differential cross sections for the reaction γp → π

π

Y . Reactions where the proton stays intact (m

=m

) are statistically separated from those where the proton dissociates to a low-mass hadronic system (m

<m

<10 GeV). The double- differential cross sections are measured as a function of the invariant mass m

of the decay pions and the squared 4-momentum transfer t at the proton vertex. The measurements are presented in various bins of the photon-proton collision energy W

. The phase space restrictions are 0.5 < m

< 2.2 GeV, | t | < 1.5 GeV

, and 20 < W

< 80 GeV. Cross section measurements are presented for both elastic and proton-dissociative scattering. The observed cross section dependencies are de- scribed by analytic functions. Parametrising the m

dependence with resonant and non-resonant contributions added at the amplitude level leads to a measure- ment of the ρ

(770) meson mass and width at m

= 770.8

(tot.) MeV and Γ

= 151.3

(tot.) MeV, respectively. The model is used to extract the ρ

(770) contribution to the π

π

cross sections and measure it as a function of t and W

. In a Regge asymptotic limit in which one Regge trajectory α(t) dominates, the intercept α(t=0) = 1.0654

(tot.) and the slope α

(t=0) = 0.233

(tot.) GeV

of the t dependence are extracted for the case m

=m

.

This publication is dedicated to the memory of our dear colleague Peter Truöl.

To be submitted to Eur. Phys. J. C

arXiv:2005.14471v3 [hep-ex] 23 Nov 2020

V. Andreev

, A. Baghdasaryan

, A. Baty

, K. Begzsuren

, A. Belousov

,

A. Bolz

, V. Boudry

, G. Brandt

, D. Britzger

, A. Buniatyan

, L. Bystritskaya

, A.J. Campbell

, K.B. Cantun Avila

, K. Cerny

, V. Chekelian

, Z. Chen

,

J.G. Contreras

, J. Cvach

, J.B. Dainton

, K. Daum

, A. Deshpande

, C. Diaconu

, G. Eckerlin

, S. Egli

, E. Elsen

, L. Favart

, A. Fedotov

, J. Feltesse

, M. Fleischer

, A. Fomenko

, C. Gal

, J. Gayler

, L. Goerlich

, N. Gogitidze

, M. Gouzevitch

, C. Grab

, A. Grebenyuk

, T. Greenshaw

, G. Grindhammer

, D. Haidt

,

R.C.W. Henderson

, J. Hladk`y

, D. Hoffmann

, R. Horisberger

, T. Hreus

, F. Huber

, M. Jacquet

, X. Janssen

, A.W. Jung

, H. Jung

, M. Kapichine

, J. Katzy

, C. Kiesling

, M. Klein

, C. Kleinwort

, R. Kogler

, P. Kostka

, J. Kretzschmar

, D. Krücker

, K. Krüger

, M.P.J. Landon

, W. Lange

,

P. Laycock

, A. Lebedev

, S. Levonian

, K. Lipka

, B. List

, J. List

, W. Li

, B. Lobodzinski

, E. Malinovski

, H.-U. Martyn

, S.J. Maxfield

, A. Mehta

, A.B. Meyer

, H. Meyer

, J. Meyer

, S. Mikocki

, M.M. Mondal

, A. Morozov

, K. Müller

, Th. Naumann

, P.R. Newman

, C. Niebuhr

, G. Nowak

, J.E. Olsson

, D. Ozerov

, S. Park

, C. Pascaud

, G.D. Patel

, E. Perez

, A. Petrukhin

,

I. Picuric

, D. Pitzl

, R. Polifka

, V. Radescu

, N. Raicevic

, T. Ravdandorj

, P. Reimer

, E. Rizvi

, P. Robmann

, R. Roosen

, A. Rostovtsev

, M. Rotaru

, D.P.C. Sankey

, M. Sauter

, E. Sauvan

, S. Schmitt

, B.A. Schmookler

,

L. Schoeffel

, A. Schöning

, F. Sefkow

, S. Shushkevich

, Y. Soloviev

, P. Sopicki

, D. South

, V. Spaskov

, A. Specka

, M. Steder

, B. Stella

, U. Straumann

, T. Sykora

, P.D. Thompson

, D. Traynor

, P. Truöl

, B. Tseepeldorj

, Z. Tu

, A. Valkárová

, C. Vallée

, P. Van Mechelen

, D. Wegener

, E. Wünsch

, J. Žáček

, J. Zhang

, Z. Zhang

, R. Žlebčík

, H. Zohrabyan

, and F. Zomer

1

I. Physikalisches Institut der RWTH, Aachen, Germany

2

School of Physics and Astronomy, University of Birmingham, Birmingham, UK

3

Inter-University Institute for High Energies ULB-VUB, Brussels and Universiteit Antwerpen, Antwerp, Belgium

4

Horia Hulubei National Institute for R&D in Physics and Nuclear Engineering (IFIN-HH) , Bucharest, Romania

5

STFC, Rutherford Appleton Laboratory, Didcot, Oxfordshire, UK

6

Institute of Nuclear Physics Polish Academy of Sciences, PL-31342 Krakow, Poland

7

Institut für Physik, TU Dortmund, Dortmund, Germany

8

Joint Institute for Nuclear Research, Dubna, Russia

9

Irfu/SPP, CE Saclay, Gif-sur-Yvette, France

10

DESY, Hamburg, Germany

11

Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germany

12

Physikalisches Institut, Universität Heidelberg, Heidelberg, Germany

13

Department of Physics, University of Lancaster, Lancaster, UK

14

Department of Physics, University of Liverpool, Liverpool, UK

15

School of Physics and Astronomy, Queen Mary, University of London, London, UK

16

Aix Marseille Université, CNRS/IN2P3, CPPM UMR 7346, 13288 Marseille, France

17

Departamento de Fisica Aplicada, CINVESTAV, Mérida, Yucatán, México

18

Institute for Theoretical and Experimental Physics, Moscow, Russia

19

Lebedev Physical Institute, Moscow, Russia

20

Max-Planck-Institut für Physik, München, Germany

21

LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France

22

LLR, Ecole Polytechnique, CNRS/IN2P3, Palaiseau, France

23

Faculty of Science, University of Montenegro, Podgorica, Montenegro

24

Institute of Physics, Academy of Sciences of the Czech Republic, Praha, Czech Republic

25

Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic

26

Dipartimento di Fisica Università di Roma Tre and INFN Roma 3, Roma, Italy

27

Institute of Physics and Technology of the Mongolian Academy of Sciences, Ulaanbaatar, Mongolia

28

Paul Scherrer Institut, Villigen, Switzerland

29

Fachbereich C, Universität Wuppertal, Wuppertal, Germany

30

Yerevan Physics Institute, Yerevan, Armenia

31

DESY, Zeuthen, Germany

32

Institut für Teilchenphysik, ETH, Zürich, Switzerland

33

Physik-Institut der Universität Zürich, Zürich, Switzerland

34

Université Claude Bernard Lyon 1, CNRS/IN2P3, Villeurbanne, France

35

Now at Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics, Moscow, Russia

36

Joint Laboratory of Optics, Palack` y University Olomouc, Czech Republic

37

Now at CERN, Geneva, Switzerland

38

Also at Ulaanbaatar University, Ulaanbaatar, Mongolia

39

Also at LAPP, Université de Savoie, CNRS/IN2P3, Annecy-le-Vieux, France

40

II. Physikalisches Institut, Universität Göttingen, Göttingen, Germany

41

Now at Institute for Information Transmission Problems RAS, Moscow, Russia

42

Brookhaven National Laboratory, Upton, New York 11973, USA

43

Department of Physics and Astronomy, Purdue University 525 Northwestern Ave, West Lafayette, IN, 47907, USA

44

Department of Physics, Oxford University, Oxford, UK

45

Rice University, Houston, USA

46

Shandong University, Shandong, P.R.China

47

Stony Brook University, Stony Brook, New York 11794, USA

†

Deceased

a

Supported by the Bundesministerium für Bildung und Forschung, FRG, under contract numbers 05H09GUF, 05H09VHC, 05H09VHF, 05H16PEA

b

Supported by the UK Science and Technology Facilities Council, and formerly by the UK Particle Physics and Astronomy Research Council

c

Supported by FNRS-FWO-Vlaanderen, IISN-IIKW and IWT and by Interuniversity Attraction Poles Programme, Belgian Science Policy

d

Partially Supported by Polish Ministry of Science and Higher Education, grant DPN/N168/DESY/2009

e

Supported by the Ministry of Education of the Czech Republic under the project INGO-LG14033

f

Supported by the Swiss National Science Foundation

g

Supported by CONACYT, México, grant 48778-F

h

Russian Foundation for Basic Research (RFBR), grant no 1329.2008.2 and Rosatom

i

Supported by the Romanian National Authority for Scientific Research under the contract PN 09370101

j

Partially Supported by Ministry of Science of Montenegro, no. 05-1/3-3352

k

Russian Foundation for Sciences, project no 14-50-00150

l

Ministery of Education and Science of Russian Federation contract no 02.A03.21.0003

1 Introduction

Diffractive hadron interactions at high scattering energies are characterised by final states consisting of two systems well separated in rapidity, which carry the quantum numbers of the initial state hadrons. Most diffractive phenomena are governed by soft, large distance processes. Despite being dominated by the strong interaction, they remain largely inaccessible to the description by Quantum Chromodynamics (QCD) in terms of quark and gluon interactions. In many cases, perturbative QCD calculations are not applicable because the typical scales involved are too low. Instead, other models have to be employed, such as Regge theory [1], in which interactions are described in terms of the coherent exchange of reggeons and the pomeron.

e

e

γ ^∗

VM

p Y

Q ²

t W _γp

Figure 1: Diffractive vector meson electroproduction.

Exclusive vector meson (VM) electroproduction e + p → e + VM + Y is particularly suited to study diffractive phenomena. This process is illustrated in Figure 1. In leading order QED, the interaction of the electron with the proton is the exchange of a virtual photon which couples to the proton in a diffractive manner to produce a VM (ρ

, ω, φ, J/ψ, . . . ) in the final state. The proton is scattered into a system Y , which can be a pro- ton ( elastic scattering) or a diffractively excited system ( diffractive proton dissociation ).

Scales for the process are provided by the vector meson mass squared m

, the photon virtuality Q

= − q

, and the squared 4 -momentum transfer at the proton vertex t, the dependence on each of which can be studied independently.

In this paper, elastic and proton-dissociative photoproduction (Q

= 0 ) of ρ

mesons is studied using electroproduction data at small Q

< 2.5 GeV

. Electroproduction of ρ

mesons has been studied previously at HERA in both the photoproduction regime and for large Q

Λ

(the perturbative cut-off in QCD), as well as for elastic and proton-dissociative scattering [2–19]. Measurements at lower photon-proton centre-of- mass energy W

have been published in fixed-target interactions [20–25]. Most recently, a measurement of exclusive ρ

photoproduction has been performed at the CERN LHC in ultra-peripheral lead-proton collisions [26].

The present measurement is based on a data set collected during the 2006/2007 HERA

running period by the H1 experiment. Since ρ

mesons decay almost exclusively into a

pair of charged pions, the analysis is based on a sample of π

π

photoproduction events.

Compared with previous HERA results, the size of the sample makes possible a much more precise measurement with a statistical precision at the percent level. It is then possible to extract up to three-dimensional kinematic distributions as a function of the invariant mass of the π

π

system m

, of W

, and of t . However, the size of the dataset is such that the systematic uncertainties of the modelling of the H1 experiment are important.

The structure of the paper is as follows: Theoretical details of ρ

meson photoproduc- tion are discussed in Section 2 with a focus on the description of π

π

photoproduction in terms of Regge theory (Section 2.1), cross section definitions (Section 2.2), and Monte Carlo modelling of relevant processes (Section 2.3). In Section 3, the experimental method is detailed, including a description of the H1 detector (Section 3.1), the dataset underlying the analysis (Section 3.2), the unfolding procedure applied to correct detector level dis- tributions (Section 3.3), and systematic uncertainties of the measurement (Section 3.4).

Results are presented in Section 4. They encompass a measurement of the integrated π

π

production cross section in the fiducial phase space (Section 4.1), a study of the invariant m

distributions (Section 4.2), measurements of the scattering energy (Sec- tion 4.3) and t dependencies of the ρ

meson production cross sections (Section 4.4), as well as the extraction of the leading Regge trajectory from the two-dimensional t and W

dependencies (Section 4.5).

2 Theory

2.1 π ⁺ π ⁻ and ρ ⁰ meson photoproduction

In electron

-proton collisions, π

π

and ρ

meson photoproduction is studied in the scat- tering process

e(e) + p(p) → e(e

) + π

(k

) + π

(k

) + Y (p

) , (1) where the 4-momenta of the participating particles are given in parentheses. The relevant kinematic variables are the electron-proton centre-of-mass energy squared

s = (e + p)

, (2)

the photon virtuality, i.e., the negative squared 4 -momentum transfer at the electron vertex

Q

= − q

= (e − e

)

, (3) the inelasticity

y = (q · p)/(e · p) , (4)

the γp centre-of-mass energy squared

W

= (q + p)

, (5)

the invariant mass of the π

π

system squared

m

= (k

+ k

)

, (6)

1

In the following, the term “electron” is used indistinctly to refer to both positrons and electrons.

the squared 4 -momentum transfer at the proton vertex

t = (p − p

)

, (7)

and the invariant mass squared of the (possibly dissociated) final state proton system

m

= (p

)

. (8)

In general, diffractive photoproduction of (light) vector mesons shares the characteris- tics of soft hadron-hadron scattering: In the high energy limit, the total and elastic cross sections are observed to rise slowly with increasing centre-of-mass energy. Differential cross sections dσ/dt are peripheral , favouring low | t |, forward scattering. With increasing scattering energy, the typical | t | of elastic cross sections becomes smaller, i.e. forward peaks appear to shrink.

In vector dominance models (VDM) [27], the photon is modelled as a superposition of (light) vector mesons which can interact strongly with the proton to subsequently form a bound VM state. Like hadron-hadron interactions in general, VM production is dominated by colour singlet exchange in the t-channel. The lack of a sufficiently hard scale makes these exchanges inaccessible to perturbative QCD in a large portion of the phase space. Empirical and phenomenological models are used instead to describe the data. At low | t | 1 GeV

, differential cross sections are observed to follow exponential dependencies dσ/dt ∝ exp(bt) . In the optical interpretation, the exponential slope b is related to the transverse size of the scattered objects. Towards larger | t | , cross section dependencies change into a less steep power-law dependence dσ/dt ∝ | t |

. In Regge theory [1], the dependence of hadronic cross sections on the scattering energy W

and the shrinkage of the forward peak are characterised by Regge trajectories α(t) . The contribution of a single Regge pole to the differential elastic cross section is dσ

/dt(W

) ∝ W

[1]. At low energies W

. 10 GeV , reggeon trajectories α

(t) dominate which are characterised by intercepts α

(0) < 1 , i.e., they result in cross sections that fall off with increasing energy [28]. In the high energy limit, only the contribution of what is known as the pomeron Regge pole remains because its trajectory α

(t) has a large enough intercept α

(0) & 1 for it not to have decreased to a negligible level. The shrinkage of the elastic forward peak with increasing energy is the result of a positive slope α

> 0 of the trajectory α(t) at t = 0 .

Feynman-like diagrams which illustrate the interpretation of ρ

meson photoproduc- tion in the VDM/Regge picture are given in Figure 2. In the diagrams, the ρ

meson is shown to decay into a pair of charged pions. This is the dominant decay channel with a branching ratio BR (ρ

→ π

π

) ' 99% [29]. The decay structure of the ρ

meson into π

π

is described by two decay angles [30]. These also give insight into the produc- tion mechanism of the ρ

meson. Contributions with s-channel helicity conservation are expected to dominate, such that the ρ

meson retains the helicity of the photon, i.e., in photoproduction the ρ

meson is transversely polarised [15].

While vector mesons dominate photon-proton interactions, the VDM approach does

not provide a complete picture. This is particularly evident for ρ

meson production where

in the region of the ρ

meson resonance peak also non-resonant π

π

production plays an

e(e)

e(e

)

p(p)

p(p

) ρ

π

(k

)

π

(k

) IP

γ

(q) Q

t

√ s

W

e(e)

e(e

)

p(p)

Y (p

) ρ

π

(k

)

π

(k

) IP

γ

(q) Q

t

√ s

W

Figure 2: Diagram of ρ

meson production and decay in elastic (left) and proton-dissociative (right) ep scattering in the VDM and Regge picture, where the interaction is governed by soft pomeron exchange in the high energy limit.

important role. The non-resonant π

π

amplitude interferes with the resonant ρ

meson production amplitude to produce a skewing of the Breit-Wigner resonance profile in the π

π

mass spectrum [31]. Newer models thus aim to take a more general approach, e.g., a recently developed model for π

π

photoproduction based on tensor pomeron exchange [32]. That model seems to be in fair agreement with H1 data when certain model parameters are adjusted [33]. A more detailed investigation is beyond the scope of this paper.

2.2 Cross section definition

2.2.1 Photon flux normalisation

In this paper, photoproduction cross sections σ

are derived from the measured electron- proton cross sections σ

. At low Q

, these can be expressed as a product of a flux of virtual photons f

and a virtual photon-proton cross section σ

:

d

σ

dydQ

= f

y, Q

σ

W

(y, Q

), Q

+ f

y, Q

σ

W

(y, Q

), Q

. (9) A distinction is made between transversely and longitudinally polarised photons, as in- dicated by the superscripts T and L , respectively. In the low Q

regime studied here, the transverse component is dominant. The transverse and longitudinal photon fluxes are given in the Weizsäcker-Williams approximation [34] by

f

(y, Q

) = α

2π 1 yQ

1 + (1 − y)

− 2(1 − y) Q

Q

(10) and

f

(y, Q

) = α

π 1

yQ

(1 − y) , (11)

respectively, where α

is the fine structure constant, m

the mass of the electron, and Q

= m

y

/(1 − y) is the smallest kinematically accessible Q

value.

In vector meson production in the VDM approach, the cross section for virtual photon interactions ( Q

> 0 ) can be related to the corresponding photoproduction cross section σ

at Q

= 0 :

σ

W

, Q

= σ

(W

)

1 + Q

m

, (12)

σ

W

, Q

= σ

W

, Q

Q

m

ξ

. (13)

In the equations, m

denotes the mass of the considered vector meson and ξ

is a proportionality constant, that in the following is set to unity. The real photoproduction cross section can then be factored out of Equation (9) according to

d

σ

dydQ

= σ

(W

(y)) ϕ

y, Q

, (14)

were the so-called effective photon flux is given by ϕ

(y, Q

) = α

2π 1 yQ

1 + (1 − y)

− 2(1 − y)

Q

Q

− Q

m

1 + Q

m

. (15) In practice, measurements of σ

are evaluated as integrals over finite regions in Q

and W

. In order to extract corresponding photoproduction cross sections at Q

= 0 and for an appropriately chosen average energy h W

i, the measured values are normalised by the effective photon flux integrated over the corresponding Q

and W

ranges:

σ

( h W

i ) = σ

Φ

, (16)

with

Φ

= Z

Q²_min< Q²< Q²_max Wmin< Wγp< Wmax

ϕ

(y, Q

) dydQ

. (17)

2.2.2 ρ

meson photoproduction cross section

With the H1 detector, π

π

photoproduction is measured. In the kinematic region stud-

ied, there are significant contributions from the ρ

meson resonance, non-resonant π

π

production, the ω meson resonance and excited ρ meson states [29, 32]. Photoproduction

of ρ

mesons has to be disentangled from these processes by analysis of the π

π

mass

spectrum. Here, a model is used which parametrises the spectrum in terms of ρ

and ω

meson, as well as non-resonant amplitudes [33], similar to the original proposal made by

Söding [31].

The contributions are added at the amplitude level, and interference effects are taken into account. The model is defined as

dσ

dm

(m

) = A q

(m

) q

(m

)

A

(m

) + A

(m

)

2

, (18)

where A is a global normalisation factor and q

(m

) describes the phase space, with q(m

) =

p

m

− 4m

being the momentum of one of the pions in the π

π

centre-of- mass frame [35]. It is normalised to the value q

(m

) at the ρ

mass. The amplitude A

takes into account the ρ

and ω meson resonance contributions, whereas the non-resonant component is modelled by A

(m

) . The components are considered to be fully coherent.

Since additional resonances with masses above 1 GeV are neglected, the model can only be applied to the region near the ρ

meson mass peak. Models of this form have been widely used in similar past analyses because they preserve the physical amplitude structure while being parametric and thus easily applicable. More sophisticated models are designed to preserve unitarity [36] or are regularised by barrier factors at higher masses [37].

The combined ρ

-ω amplitude is modelled following a parametrisation given by [38]

A

(m

) = BW

(m

)

1 + f

e

m

m

BW

(m

)

, (19)

where f

and φ

are a normalisation factor and a mixing phase for the ω contribution, respectively. The ω meson is not expected to decay into a pair of charged pions directly because of the conservation of G-parity by the strong interaction. However, electromag- netic ω → ρ

-mixing with a subsequent ρ

→ π

π

decay is possible [39]. Both resonances are modelled by a relativistic Breit-Wigner function [40]:

BW

(m

) = m

Γ

m

− m

+ i m

Γ(m

) . (20) The parameters m

and Γ

are the respective vector meson’s Breit-Wigner mass and width. The Breit-Wigner function is normalised to |BW

(m

) | = 1 . For the ρ

resonance a p-wave mass-dependent width [35] is used:

Γ(m

) = Γ

q

(m

) q

(m

)

m

m

, (21)

whereas a constant width is assumed for the very narrow ω resonance.

The unknown non-resonant amplitude is parametrised by the function A

(m

) = f

(m

− 4m

+ Λ

)

, (22)

where the relative normalisation is given by f

, while Λ

and δ

are free model param-

eters. They can shape the amplitude for the modelling of a possible internal structure

of the non-resonant γππ-coupling. In similar past analyses, typically a purely real non-

resonant amplitude has been assumed. Following that assumption, f

is set to be real.

For δ

>

, the non-resonant contribution to the cross section (cf. Equation (18)) has a local maximum at

m

= q

Λ

+ (

δ

− 1) 4m

q

3

δ

− 1

, (23)

and falls proportionally to (1/m

)

in the high mass region.

In order to extract the ρ

meson contribution to the π

π

photoproduction cross section, the measured π

π

mass distributions are fitted using Equation (18). The ρ

meson Breit-Wigner contribution is then conventionally defined by the integral

σ(γp → ρ

Y ) = A q

(m

)

Z

2mπ

BW

(m)

q

(m)dm. (24)

As the ρ

meson resonance decays almost exclusively into two charged pions, this is taken to be equal to the total ρ

meson photoproduction cross section without correcting for the ρ

→ π

π

branching fraction.

Kinematic dependencies of the ρ

meson production cross section on the variables W

, t, and m

are measured by fitting the mass distributions in bins of the respective variables, such that all model parameters may have kinematic dependencies. Physical considerations and statistical and technical limitations affect the assumed dependencies.

Physical parameters, i.e., m

, Γ

, and δ

are assumed to be constants. The small width of the ω meson cannot be constrained by the present data and the PDG value Γ

= 8.5 MeV [29] is assumed and kept fixed in all fits. Dependencies of f

, φ

, and f

on t or W

cannot be constrained with the present data. However, these parameters are allowed to depend on m

, i.e., to be different for elastic and proton-dissociative distributions. The non-resonant background is observed to change with t. This is modelled by a t dependence of the parameter Λ

, which also can be different for elastic and proton- dissociative distributions. The normalisation A is a free parameter in each kinematic bin.

All fit set-ups with the corresponding parameter assumptions are summarised in Table 1.

2.3 Monte Carlo modelling

For the purpose of quantifying detector effects, the data are modelled using Monte Carlo (MC) simulations of elastic and proton-dissociative electroproduction of ρ

, ω(782) , φ(1020) , ρ(1450) , and ρ(1700) vector mesons, as well as for non-resonant diffractive photon dissociation. The samples are all generated using the DIFFVM event generator [41]

that models VM production on the principles of equivalent photon approximation [34], VDM [27], and pomeron exchange [42]. Proton dissociation is modelled by DIFFVM assuming the following dependence of the cross section on the mass of the dissociated system:

dσ

dm

= f (m

)

(m

)

. (25)

Here,

= 0.0808 and f (m

) is a phenomenological function that is fitted to the

experimental data [43] to parametrise the low-mass resonance structure in the region

Number of free fit parameters

Parameter Dependencies

(m; m

)

(m; m

, W )

(m; m

, t)

(m; m

, W, t) A m

, W, t 1

+ 1

9

+ 6

12

+ 9

4

· 7

+ 4

· 5

m

- 1 1 1 1

Γ

- 1 1 1 1

f

m

1

+ 1

fixed fixed fixed

φ

m

1

+ 1

fixed fixed fixed

m

- 1 fixed fixed fixed

Γ

- PDG PDG PDG PDG

f

m

1

+ 1

1

+ 1

1

+ 1

1

+ 1

δ

- 1 1 1 1

Λ

m

, t 1

+ 1

1

+ 1

12

+ 9

7

+ 5

Total 14 22 47 65

Table 1: Parameter assumptions and resulting number of parameters used to fit Equation (18) to the invariant π

π

mass distributions. The number of parameters depends on the number of bins in the extracted cross sections. The number of bins in which a parameter is fitted freely is given and the corresponding distribution indicated by sub- and superscripts. For the fits of the m

distributions in multiple W

or t bins, the ω meson model parameters are fixed to the values obtained from the fit to the one-dimensional distributions. The ω meson width is always fixed to the PDG value.

m

< m

< 1.9 GeV . For m

> 1.9 GeV , the function f(m

) = 1 becomes constant. In the low mass region the dissociative system is treated as an N

resonance and decays are modelled according to measured branching fractions [29]. For higher masses the decay is simulated using the Lund fragmentation model as implemented in JETSET [44]. Non- resonant photon dissociation is modelled analogously by assuming a dissociative mass m

spectrum dσ

/dm

= 1/(m

)

with

=

, and simulating the decay using the Lund model.

In Table 2, details on the samples and in particular on the simulated decay modes are listed

. Several of the considered processes result in an exclusive π

π

final state. They are simulated by DIFFVM independently, so that interference effects are not considered.

However, these can be significant. For example, the interference between the ρ

meson resonance and non-resonant π

π

production causes a strong skewing of the resonance lineshape. To consider these interference effects, the ρ

meson samples are reweighted to describe exclusive π

π

production including contributions from ρ

, ω , and a single ρ

meson resonance and non-resonant production, that are all added at the amplitude level. For the reweighting, a t and m

dependent lineshape is used, which is similar to the model introduced in Section 2.2.2 but is extended by an additional ρ

Breit-Wigner amplitude [33].

All generated events are passed through the full GEANT-3 [45] based simulation of

2

For the simulation of the ρ(1450) and ρ(1700) mesons, DIFFVM was modified to account for the

finite width of intermediate ρ(770) resonances, and decay modes involving the final state π

π

π

π

were

added.

Number of events

Process Decay modes BR [%] elastic p-dissociative

ρ

(770) π

π

99.0

10

10

π

π

γ 1.0

, → reweighted to describe all π

π

final states

ω(782)

π

π

π

89.2

10

10

π

γ 8.6

π

π

(removed, included in signal) 2.2

φ(1020)

K

K

49.0

10

10

K

K

34.4

π

ρ

, π

ρ

, π

ρ

4.3, 4.3, 4.3

π

π

π

2.4

ηγ 1.3

ρ(1450) ρ

π

π

, ρ

π

π

, ρ

π

π

25.0, 25.0, 25.0

10

10

& π

π

π

π

15.0

ρ(1700) π

π

π

π

8.0

10

10

π

π

(removed, included in signal) 2.0

, → merged ρ(1450) : ρ(1700) = 1 : 1 γ -dissoc. Lund fragmentation model

10

10

(exclusive π

π

removed, included in signal)

Table 2: DIFFVM MC samples used to model the π

π

photoproduction dataset. All decay modes with a branching fraction & 1% are simulated [41]. For the ρ(1450) and ρ(1700) samples a ratio of 1:1 is assumed. The π

π

final states are removed from background samples and included in the signal definition.

the H1 apparatus and are reconstructed using the same program chain as used for the data. Trigger scaling factors are applied to correct differences in the trigger performance between data and simulation. They are obtained from a π

π

electroproduction sample, that is triggered independently of the tracking devices [33].

A template is constructed from all MC samples to describe the data. For a better description of the W

and t distributions, all samples are tuned to data [33]. An additional background contribution from beam-gas events is estimated in a data driven method.

The MC normalisations are obtained from data control regions that are enriched with events from a given process through modified event selection requirements as described below. The ρ(1450) and ρ(1700) samples cannot be well distinguished experimentally in this analysis. They are thus combined at a 1:1 ratio and treated as a single MC sample. In order to obtain normalisations for the elastic and proton-dissociative samples independently, information from the forward detector components is used as described below.

Neither initial and final state radiation of real photons from the electron, nor vacuum

polarisation effects are simulated. Consequently, these effects are not corrected for in

the present measurement. In a comparable phase space, their effect on the overall cross section has been estimated to be smaller than 2% [46].

3 Experimental Method and Data Analysis

3.1 H1 detector

A detailed description of the H1 detector is given elsewhere [47, 48]. The components that are relevant for the present analysis are briefly described in the following. A right-handed Cartesian coordinate system is used with the origin at the nominal ep interaction point.

The proton beam direction defines the positive z -axis ( forward direction ). Transverse momenta are measured in the x-y plane. Polar (θ) and azimuthal (φ) angles are measured with respect to this frame of reference.

The interaction point is surrounded in the central region ( 15

< θ < 165

) by the central tracking detector. Two large coaxial cylindrical jet chambers (CJC1 and CJC2) for precise track reconstruction form its core. They are supported by the central inner proportional chamber (CIP) used for the reconstruction of the primary vertex position on the trigger level, a z-drift chamber for an improved reconstruction of z coordinates, and a silicon vertex detector for the reconstruction of secondary decay vertices [49]. In the forward direction ( 7

< θ < 30

), additional coverage is provided by the forward track- ing detector, a set of planar drift chambers. The tracking detectors are operated in a solenoidal magnetic field of 1.16 T. For offline track reconstruction, track helix parame- ters are fitted to the inner detector hits in a general broken lines fit [50]. The procedure considers multiple scattering and corrects for energy loss by ionisation in the detector material. The primary vertex position is calculated from all tracks and optimised as part of the fitting procedure. Transverse track momenta are measured with a resolution of σ(p

)/p

' 0.002 p

/GeV ⊕ 0.015 . The CJCs also provide a measurement of the specific energy loss of charged particles by ionisation dE/dx with a relative resolution of 6.5% for long tracks.

The tracking detectors are surrounded by the liquid argon (LAr) sampling calorime- ter [51]. It provides coverage in the region 4

< θ < 154

and over the full azimuthal angle. The inner electromagnetic section of the LAr is interlaced with lead, the outer hadronic section with steel absorbers. With the LAr, the energies of electromagnetic and hadronic showers are measured with a precision of σ(E)/E ' 12%/ p

E/GeV ⊕ 1% and σ(E)/E ' 50%/ p

E/GeV ⊕ 2% , respectively [52]. In the backward region ( 153

< θ < 178

), energies are measured with a spaghetti calorimeter (SpaCal) of lead absorbers interlaced with scintillating fibres [48].

Detector components positioned in the very forward direction are used in this analysis

to identify proton dissociation events. These are the forward muon detectors (FMD),

the PLUG calorimeter and the forward tagging system (FTS). The lead-scintillator plug

calorimeter is positioned around the beampipe at z = 4.9 m to measure the energies of

particles in the pseudorapidity region 3.5 < η < 5.5 . The FMD is a system of six drift

chambers positioned outside of the LAr and covering the range 1.9 < η < 3.7 . Particles at larger pseudorapidity up to η . 6.5 can still induce spurious signals via secondary particles produced in interactions with the beam transport system and detector support structures [53]. The very forward region, 6.0 < η < 7.5 , is covered by an FTS station of scintillation detectors positioned around the beampipe at z = 28 m .

The H1 trigger is operated in four stages. The first trigger level (L1) is implemented in dedicated hardware reading out fast signals of selected sub-detector components. Those signals are combined and refined at the second level (L2). A third, software-based level (L3) combines L1 and L2 information for partial event reconstruction. After full detector read-out and full event reconstruction, events are subject to a final software-based filtering (L4). The data used for the present analysis are recorded using mainly information from the fast track trigger (FTT) [54]. The FTT makes it possible to measure transverse track parameters at the first trigger level and complete three-dimensional tracks at L2. This is achieved through applying pattern recognition and associative memory technology to identify predefined tracks in the hit-patterns produced by charged particles in a subset of the CJC signal wires.

The instantaneous luminosity is measured by H1 with a dedicated photon detector located close to the beampipe at z = − 103 m . With it, the rate of the Bethe-Heitler process ep → epγ is monitored. The integrated luminosity is measured more precisely with the main H1 detector using the elastic QED Compton process. In this process, the electron and photon in the epγ final state have large transverse momenta and can be reconstructed in a back-to-back topology in the SpaCal. The integrated luminosity has been measured with a total uncertainty of 2.7% [55] that is dominated by systematic effects.

3.2 Data sample

The present analysis is based on data collected by the H1 experiment during the 2006/2007 HERA running period. In that period, the accelerator was operated with positrons hav- ing an energy of E

= 27.6 GeV and protons with an energy of E

= 920 GeV . Due to bandwidth limitations, only a subset of the H1 dataset is available for the trigger conditions relevant for this analysis, corresponding to an effective integrated luminosity of L

= 1.3 pb

. In the kinematic range considered in this analysis, the pions from ρ

→ π

π

photoproduction are produced within the acceptance of the CJC and with low transverse momenta p

. 0.5 GeV . In the diffractive photoproduction regime, both the outgoing proton and electron avoid detection by escaping through the beampipe

.

3.2.1 Trigger

A dedicated, track-based π

π

photoproduction trigger condition was used for online event selection. Track information within the 2.3 µs decision time of the L1 trigger was

3

In the studied energy region, the elastically scattered protons are mostly outside of the acceptance re-

gion of the H1 forward proton spectrometer (FPS) and the very forward proton spectrometer (VFPS) [56].

available through the FTT. For a positive trigger decision, at least two FTT tracks above a transverse momentum threshold of 160 MeV and at most three tracks above a threshold of 100 MeV were required. The sum of the charges of these tracks was restricted to

± 1 elementary electric charge. In addition, trigger information from the CIP was used to ensure a low multiplicity interaction within the nominal interaction region along the z -axis.

Vetoes on the inner forward part of the LAr calorimeter and on a scintillator wall in the forward direction were applied to suppress non-diffractive inelastic interactions. Further SpaCal and timing vetoes rejected events from beam-gas and beam-machine interactions.

To keep under control the expected rate from the large ρ

meson production cross section, the trigger was scaled down by an average factor of ∼ 100 .

3.2.2 Event reconstruction and selection

In order to select a sample of π

π

photoproduction events, a set of offline selection cuts is applied on top of the trigger requirements:

• The π

π

topology is ensured by requiring exactly two primary-vertex fitted, cent- ral tracks to be reconstructed. They need to satisfy some additional quality re- quirements, have opposite charge, and be within the acceptance region

defined as 25

< θ < 155

and p

> 0.16 GeV . Low-momentum kaons, protons, and deuterons are suppressed using the difference between the measured energy loss dE/dx of the tracks in the CJC and the expected loss for the respective particle hypothesis in a likelihood-based approach. The two tracks are then taken to be the pion candi- dates, and their 4-momentum vectors are calculated with the corresponding mass hypothesis.

• The photoproduction kinematic regime is ensured by vetoing events with a scattered electron candidate in the SpaCal or LAr. The SpaCal acceptance then limits the photon virtuality to Q

. 2.5 GeV

.

• The diffractive topology is ensured by requiring a large rapidity gap between the central tracks and any forward detector activity. Events with LAr clusters above a noise level of 0.6 GeV in the forward region θ < 20

are rejected. Information from the FTD is used to reconstruct forward tracks, and events with more than one forward track that cannot be matched to one of the central tracks are also rejected.

The presence of a single unmatched track is permitted to reduce the sensitivity on the modelling of the forward energy flow in the forward detectors. This rapidity gap selection in particular also limits the mass of the proton-dissociative system to approximately m

. 10 GeV .

• Background processes with additional neutral particles or charged particles outside of the central tracker acceptance are suppressed by cuts on the LAr and SpaCal energy. LAr and SpaCal clusters above respective noise levels of 0.6 GeV and 0.3 GeV are geometrically matched to the two central tracks: A cluster is associated

4

The polar acceptance is reduced with respect to the CJC geometry to improve the performance of

the π

π

photoproduction trigger and its MC simulation.

to a track if it is within a cylinder of a 60 cm radius in the direction of the track upon calorimeter entry. The energies from clusters not associated to either track are summed up. Events are rejected if the total unassociated LAr or SpaCal energies exceed thresholds of 0.8 GeV or 0.4 GeV , respectively. This allows for a small amount of unassociated energy to account for residual noise or secondary particles produced in interactions of the pion candidates with the detector material. A further suppression of background events with additional final state particles is achieved by requiring a transverse opening angle between the two pion tracks ∆φ > 50

.

• For a reliable trigger performance and MC modelling thereof, the difference in the FTT track angles

must exceed ∆φ

> 20

.

• The background is further reduced by rejecting out-of-time events via cuts on the LAr and CJC event timing information. Background events from beam-gas and beam-wall interactions are suppressed by restricting the z coordinate of the primary vertex to be within 25 cm of the nominal interaction point.

The reaction ep → eπ

π

Y is kinematically underconstrained since only the two pions in the final state are reconstructed. The mass of the π

π

system m

is reconstructed from the 4-momenta of the two tracks under pion hypothesis. The momentum transfer at the proton vertex t and the scattering energy W

are reconstructed from the two pion 4-momenta:

t

= − p

(26) and

W

= q

2E

E

− p

. (27)

Here, E

denotes the proton-beam energy and E

, p

, and p

are the measured energy, transverse, and longitudinal 4-momentum components of the π

π

system. These two equations are approximations to Equation (5) and Equation (7), respectively. In some regions of the probed phase space, Q

may be similar in size to t , or m

may be similar in size to W

, such that these approximations are poor. Such effects are corrected for in the unfolding procedure discussed later in the text (cf. Section 3.3).

The analysis phase space probed by this measurement is explicitly defined by detector- level cuts 15 < W

< 90 GeV , t

< 3 GeV

, and 0.3 < m

< 2.3 GeV . The exclusivity requirements, which veto events with detector activity not related to the π

π

pair, further restrict the phase space to Q

. 2.5 GeV

and m

. 10 GeV . The mean and median Q

in that phase space are approximately 0.02 GeV

and 8 · 10

GeV

, respectively, as evaluated in the MC simulation.

A total of 943 962 π

π

photoproduction event candidates pass all selection require- ments. In Figure 3, the selected number of events is shown as a function of m

, W

, and t

. The distributions are compared to the MC model introduced in Section 2.3. The ρ

meson resonance at a mass of ∼ 770 MeV clearly dominates the sample. Background contamination amounts to about 11% and is investigated in the next section.

5

The FTT φ angle is determined at a radial distance of r = 22 cm from the z axis.

3.2.3 Background processes

The π

π

photoproduction sample includes various background contributions, even after the full event selection. The dominant background processes are the decays of diffrac- tively produced ω → π

π

π

, φ → K

K

, or ρ

→ 4π, as well as diffractive photon dissociation. Another source of background originates from interactions of the electron and proton beams with residual gas. Such reducible background events are wrongly se- lected when charged kaons or protons are misidentified as pions or additional charged or neutral particles escape detection, e.g., by being outside the central tracker acceptance or having energies below the calorimeter noise threshold. In addition to the ρ

meson, some other vector mesons also decay to an exclusive π

π

state (cf. Table 2). Rather than being treated as irreducible background, these are included in the signal for the analysis of the π

π

production cross section.

To study the reducible background contributions in more detail, multiple dedicated control regions are introduced:

• ω(782) mesons predominantly decay into the π

π

π

final state. The π

meson can be identified via energy deposits in the calorimeters that are not associated with either of the two pion tracks. An ω control region is defined by replacing the empty calorimeter selection by a cut E

> 0.8 GeV on the unassociated energy deposited in the LAr. Events with an ω meson are distinguished from those with a ρ

meson by cuts on m

< 0.55 GeV and on the invariant mass of both tracks (assumed to be pions) and all unassociated clusters m

< 1.2 GeV . The ω meson purity achieved in this region is roughly 54%.

• φ(1020) mesons predominantly decay into pairs of charged kaons. A φ control region is defined by replacing the dE/dx pion identification selection cuts by a kaon selection and requiring the invariant K

K

mass to be within 15 MeV of the φ meson mass. Also the cut on the opening angle between the two tracks at the vertex is removed. The φ meson purity achieved in this region is roughly 89%.

• The excited ρ

meson dominantly decay into 4 pions in various charge configurations.

Due to the track veto in the trigger, additional tracks cannot be used to identify ρ

→ 4π events. Instead, unassociated energy deposits in the LAr E

> 0.8 GeV are required in place of the empty LAr signal selection. Events with a ρ

meson are distinguished from those with an ω meson by requiring m

> 1.2 GeV . The ρ

meson purity achieved in this region is roughly 48%.

• Particles from photon dissociation emerge primarily in the backwards direction. A photon dissociation control region is thus defined by replacing the empty SpaCal signal requirement by a cut 4 < E

< 10 GeV on the unassociated energy deposit in the SpaCal. The lower cut removes ω and ρ

events, the upper cut is retained as a veto against the scattered electron. The photon dissociation purity achieved in this region is roughly 78%.

For the ρ

meson photoproduction cross section measurement, reducible background

processes are subtracted in the unfolding procedure, where the templates for the respective

diffractive background processes are taken from the DIFFVM MC samples, as described in Section 2.3. The respective normalisation factors are determined by making use of the control regions in the unfolding process. The residual beam-gas induced background is modelled in a data driven approach, using events from electron and proton pilot bunches.

For electron (proton) pilot bunches, there is a corresponding gap in the proton (electron) beam bunch structure, such that only interactions with rest-gas atoms may occur. The beam gas background shape predictions estimated from pilot bunch events are scaled to match the integrated beam current of the colliding bunches. The beam-gas induced background amounts to about 2%.

3.2.4 Proton dissociation tagging

In proton-dissociative events, the proton remnants are produced in the very forward di- rection where the H1 detector is only sparsely instrumented. Consequently, the remnants cannot be fully reconstructed, and elastic and proton-dissociative scattering cannot be uniquely identified on an event-by-event basis. However, in many cases some of the remnants do induce signals in the forward instruments, either directly or via secondary particles that are produced in interactions with the detector or machine infrastructure.

These signals are used to tag proton-dissociative events ( tagging fraction ). At a much lower level, such signals can also be present in elastic scattering events ( mistagging frac- tion ), e.g., in the presence of detector noise or when the elastically scattered proton produces secondaries in interactions with the beam transport system. By simulating the respective tagging and mistagging fractions of proton-dissociative and elastic scattering, the respective proton-dissociative and elastic contributions to the cross section can be determined.

The forward detectors used for tagging in this analysis are the FMD, the PLUG, and the FTS. An event is considered to be tagged by the FMD if there is at least one hit in any of the first three FMD layers, by the PLUG if there is more than one cluster above a noise level of 1.2 GeV , or by the FTS if it produces at least one hit. A small contribution to the FTS signal, induced by secondary particles produced by the elastically scattered proton hitting a beam collimator, is discarded by applying acceptance cuts depending on t

and the location of hits in the FTS [33].

The tagging information from the three detectors is combined by summing the total number of tags in an event: 0 ≤ N

≤ 3 . In turn, three tagging categories are defined:

a zero-tag (N

= 0 ), single-tag (N

= 1 ), and multi-tag (N

≥ 2 ) category. The respective tagging fractions for events passing the standard selection cuts are shown in Figure 4 as a function of t

. The tagging categories are used to split the dataset into 3 tagging control regions. The zero-tag region is dominated by ∼ 90% elastic events, in the single-tag region their fraction is reduced to ∼ 64% , and in the multi-tag region proton dissociation dominates at ∼ 91% .

3.3 Unfolding

An unfolding procedure is applied to correct binned reconstructed detector-level distri-

butions for various detector effects. The unfolding corrects the data for reducible back-

Analysis phase space Fiducial measurement phase space 15.0 < W

< 90.0 GeV

| t | < 3.0 GeV

0.3 < m

< 2.3 GeV

Q

< 2.5 GeV

m

< 10.0 GeV

20.0 < W

< 80.0 GeV

| t | < 1.5 GeV

0.5 < m

< 2.2 GeV

Q

< 2.5 GeV

elastic: m

= m

p-dissociative: m

< m

< 10.0 GeV

Table 3: Analysis and fiducial measurement phase space. At detector level, the respective cuts are applied to W

, t

, and m

, the Q

cut is replaced by the veto on the reconstruction of the scattered electron, and the m

cut is replaced by the rapidity gap requirement as detailed in the text.

ground contributions, the finite resolution of reconstructed variables, and efficiency and acceptance losses. Furthermore, it is set up to separate elastic and proton-dissociative scattering events. This makes possible the determination of elastic and proton-dissociative particle level distributions from which the corresponding differential π

π

photoproduc- tion cross sections are derived. The cross sections are measured in a fiducial phase space that is slightly smaller than the analysis phase space defined by the event selection. This makes it possible to account for contributions migrating into and out of the fiducial phase space. The fiducial and analysis phase space cuts are summarised in Table 3.

3.3.1 Regularised template fit

Differential cross section measurements are performed for various distributions of the variables m

, W

, and t, and combinations thereof. The beam-gas background template is subtracted from the considered data distribution and the result is used as input to the unfolding. The unfolding is performed by means of a regularised template fit within the TUnfold framework [57]. A response matrix A is introduced, with elements A

describing the probability that an event generated in bin j of a truth-level distribution ~x

is reconstructed in bin i of a detector-level distribution ~y. In the definition of the response

matrix, elastic and proton-dissociative signal and background MC processes are included

as dedicated sub-matrices. This makes it possible to separate the elastic and proton-

dissociative signal components in the unfolding. Also, background subtraction is implicitly

performed during the unfolding where the normalisation of the backgrounds is determined

in the fit. At detector level, the response matrix is split into signal and background control

regions as defined above. The signal region is further split into three and the background

regions into two orthogonal forward tagging categories. This constrains the respective

MC contributions in the template fit. Migrations into and out of the fiducial phase space

are considered by including side bins in each sub-matrix both at detector and at truth

level [33]. These contain events passing the analysis phase space cuts but failing the

fiducial cuts (cf. Table 3). As an illustration, the response matrix used for unfolding the

one-dimensional m

distributions is given in Figure 5. For all response matrices, most

truth bins are found to have good constraints by at least one reconstruction level bin with